Optimized Baxter model of protein solutions: Electrostatics versus adhesion

Abstract

A theory is set up of spherical proteins interacting by screened electrostatics and constant adhesion, in which the effective adhesion parameter is optimized by a variational principle for the free energy. An analytical approach to the second virial coefficient is first outlined by balancing the repulsive electrostatics against part of the bare adhesion. A theory similar in spirit is developed at nonzero concentrations by assuming an appropriate Baxter model as the reference state. The first-order term in a functional expansion of the free energy is set equal to zero which determines the effective adhesion as a function of salt and protein concentrations. The resulting theory is shown to have fairly good predictive power for the ionic-strength dependence of both the second virial coefficient and the osmotic pressure or compressibility of lysozyme up to about 0.2 volume fraction.

Liquid−Liquid Coexistence Surface for Lysozyme: Role of Salt Type and Salt Concentration

“…Note that, for NaCl, the second virial coefficient is decreasing as a function of salt concentration, while, for MgCl 2 , the second virial coefficient first decreases and then increases with salt concentration. The line from the model for NaCl at pH ) 4.0 follows closely with experimental data for pH ≈ 4.5 compiled from various sources in ref 23. It is important to note that we use a model with a shortrange attraction, a square well with λ ) 1.15, in a regime where the net lysozyme interaction is attractive.…”

Collective diffusion coefficient of proteins with hydrodynamic, electrostatic, and adhesive interactions

“…In this case, we do this by matching the respective second virial coefficients, which ensures that the free energy of the two systems at small concentrations are identical. We emphasize that in the general case, at arbitrary concentrations, we have to match the complete free energies of the respective systems; 32,33 it is then incorrect to focus on the second virials as has often been done in the past.…”

“…The added salt is NaCl and in most cases, a small amount of Na acetate has been added as buffer. The reason for choosing lysozyme under these conditions is that we have previously evaluated the range and strength of the short-range attraction 32 and a lot of experimental data on the collective diffusion coefficient are available in the literature ͑see Fig. 3͒.…”

“…We first introduce the interaction used previously to compute protein solution properties 32 and give expressions for the effective stickiness. We then outline the formal expression for C due to Felderhof 23 in terms of the pair potential between two protein spheres and a hydrodynamic mobility function.…”

“…17 In Ref. 32, we approximated globular proteins in water with added monovalent salt by hard spherical particles that interact through a short-range attraction and a screened electrostatic repulsion. We appropriately replaced this system by one of spherical particles with sticky interactions only.…”